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Newest items, query logic

Hi
I want a query that does the following thing,
Select the 10 latest items added in my database, but only the latest item of each category.
databaselayout:
Category
id, name
Item
id, name, dateadded, categoryid

Query should be something like :
select * from Item
group by categoryid
having count(categoryid)=1
order by dateadded desc
limit 0,10

but I get 0 rows returned.. What's wrong with my query logic?
thanks in advance!